Wood displacement for 3D Print
I edit this answer to be better than previous and to actually work for 3D-printing. This is going to be a long one. This works for procedural textures and for ones made with a displacement map. You could try to start from step 6 If you have a good displacement map but for some reason it didn't work for me.

At first I have a plane with 5x Subdivision Surface Modifier and a Displacement Map image connected to the Material Output Through a Viewer. Color Space Non-Color



Next I add an Image Texture node but don't connect it. Select New and adjust Width and Height to be 8192 px. This can be lower if you are ok with lower quality. Check the 32 bit Float box.



Render Engine Cycles. Device CPU (You could use GPU but for me Blender crashes when I try that). In Sampling Render 1 (You don't need more. It just slows down.) In Performance and Tiles Tiles X and Tiles Y should be the same as the image size you created earlier. In my case it is 8192 px x 8192 px. Color-Space Non-Color



Under Bake select bake type to Emit. Make sure the lonely Image Texture node is selected and press Bake.



Go to Image Editor and select Image and Save As. File Format OpenEXR and Color Depth Float (Full). Save As Image.



Give your plane a Subdivision Surface modifier with Level 5 or 6. 6 is better. If this is not enough you can always add More. Modifier type should be Simple. Give it also a Displace modifier and press New.



Press Show texture in Texture tab.



Press Open and find your saved image



Deselect Half Float Precision and go back to Modifiers panel.



Change Displace Modifier Coordinates to UV and Decrease the Strength. If the displacement is wrong you can change the direction to RGB to XYZ but this shouldn't be the case if your images are in non-color format.



Select your object and Export Stl.



Check Selection Only and Apply Modifiers.



Now you have a stl with your displacement.